x_matrix <- matrix(data=NA, nrow=256, ncol=4)
x_matrix[, 1] <- rep(1:4, times = 1, length.out = NA, each = 64)
x_matrix[, 2] <- rep(1:4, times = 4, length.out = NA, each = 16)
x_matrix[, 3] <- rep(1:4, times = 16, length.out = NA, each = 4)
x_matrix[, 4] <- rep(1:4, times = 64, length.out = NA, each = 1)
sd(rowMeans(x_matrix))